A company sells two products with information as follows: $$\begin{array} { | l | r | r | }
\hline &{ \text { A } } & { \text { B } } \
\hline \text { Price per unit } & \$ 12 & \$ 20 \
\hline \text { Variable cost per unit } & \$ 10 & \$ 12 \
\hline
\end{array}$$ Products are made by machine. 4 units of Product A can be made with one machine hour and 2 units of Product B can be made with one machine hour. The company has a maximum of 3,000 machine hours available per month. Assume there are no constraints on sales of either product, and the company could choose any product mix they wish. What is the maximum amount of contribution margin that the company could earn in a month?

Question

A company sells two products with information as follows: $$\begin{array} { | l | r | r | } 
\hline &{ \text { A } } &  { \text { B } } \
\hline \text { Price per unit } & \$ 12 & \$ 20 \
\hline \text { Variable cost per unit } & \$ 10 & \$ 12 \
\hline
\end{array}$$ Products are made by machine. 4 units of Product A can be made with one machine hour and 2 units of Product B can be made with one machine hour. The company has a maximum of 3,000 machine hours available per month. Assume there are no constraints on sales of either product, and the company could choose any product mix they wish. What is the maximum amount of contribution margin that the company could earn in a month?

Quizplus · Accepted Answer

To maximize the contribution margin, the company should produce the product with the highest contribution margin per machine hour.

Product A has a contribution margin of $2 per unit ($12 - $10) and requires 4 machine hours per unit, so its contribution margin per machine hour is $0.50 ($2/4).

Product B has a contribution margin of $8 per unit ($20 - $12) and requires 2 machine hours per unit, so its contribution margin per machine hour is $4 ($8/2).

Therefore, the company should focus on producing Product B as it has the higher contribution margin per machine hour.

With 3,000 machine hours available per month, the maximum number of units of Product B that can be produced is:

3,000 machine hours/month x 1 unit/2 machine hours = 1,500 units/month

The contribution margin from selling 1,500 units of Product B is:

1,500 units x $8/unit = $12,000

Therefore, the maximum amount of contribution margin that the company could earn in a month is $12,000.

However, this assumes that the company can sell 1,500 units of Product B at the given price. If there are constraints on demand, then the company will need to adjust its production plan accordingly.

A Company Sells Two Products with Information as Follows Products Are Made by Machine